SSR {StressStrength}

Computation of reliability of stress-strength models

Description

For a stress-strength model, with independent r.v. X and Y representing the strength and the stress respectively, the function computes the reliability R=P(X>Y)

Usage

SSR(parx, pary, family = "normal")

Arguments

parx

parameters of X distribution (for the normal distribution, mean \mu_x and standard deviation \sigma_x)

pary

parameters of Y distribution (for the normal distribution, mean \mu_y and standard deviation \sigma_y)

family

family distribution for both X and Y (now, only "normal" available)

Details

The function computes R=P(X>Y) where X and Y are independent r.v. following the family distribution with distributional parameters parx and pary.

Value

R=P(X>Y). For normal distributions, R=\Phi(d) with d=(\mu_x-\mu_y)/\sqrt{\sigma_x^2+\sigma_y^2}.

Author(s)

Alessandro Barbiero, Riccardo Inchingolo

References

Kotz S, Lumelskii Y, Pensky M (2003) The stress-strength model and its generalizations: theory and applications. World Scientific, Singapore

See Also

estSSR

Examples

# let X be a normal r.v. with mean 1 and sd 1;
# and Y a normal r.v. with mean 0 and sd 2
# X and Y independent
parx<-c(1, 1)
pary<-c(0, 2)
# reliability of the stress-strength model (X=strength, Y=stress)
SSR(parx,pary)
# changing the parameters of Y
pary<-c(1.5, 2)
# reliability of the stress-strength model (X=strength, Y=stress)
SSR(parx,pary)